The structural biocomplexity of two viral structures is evaluated: that of the small RNA tobacco mosaic virus (TMV) and that of the larger dsDNA bacteriophage T4. Tobacco mosaic virus was chosen as a paradigm of a self-organizing biostructure, while the T4 represents biostructures where genome directed instructions are essential for the achievement of the correct virion structure. A large difference in complexity values is found: C = 4 for the TMV virion versus C = 117 for the tail part of the T4 virion. The considerable difference in these values indicates a correlation between the structural biocomplexity as defined and the pattern coding requirements of these organisms. It is proposed to utilize complexity analysis for the evaluation of expected genomic contribution to structural specification: the higher the complexity of a structure, the more genomic directions, of known or unknown nature, are likely to be required. The elements of biological complexity evaluation (Yagil, 1985; 1993b) are briefly summarized. A quantitative measure of order (0.93 for the T4 tail fiber) is an additional outcome of the formalism employed.